# How do you graph the system #x>5# and #y<=4#?

See the explanation.

graph{x > 5 [-4.585, 17.915, -4.465, 6.785]}

graph{y <=4 [-5.99, 19.32, -5.17, 7.49]}

The conjunction ("and") requires both to be true, so we need the part of the plane where these overlap. That is: we need the part that is shaded on both graphs:

(I had to use a different graphing utility, so the colors are different and you cannot scroll this graph.)

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To graph the system ( x > 5 ) and ( y \leq 4 ), you would start by graphing the line ( x = 5 ) as a vertical line passing through the point ( (5, 0) ) on the x-axis. Then, since ( x > 5 ), you would shade the area to the right of this line. Next, graph the line ( y = 4 ) as a horizontal line passing through the point ( (0, 4) ) on the y-axis. Since ( y \leq 4 ), you would shade the area below this line. The shaded region where both conditions are met represents the solution to the system of inequalities.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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